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Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices

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  • Abdul Shakoor
  • Hu Yang
  • Ilyas Ali

Abstract

We give a formula of (P + Q) D under the conditions P2Q + QPQ = 0, P3Q = 0, and PQPQ = 0. Then, we apply it to give some expressions for the Drazin inverse of block matrix M=(ABCD) (A and D are square matrices) under some conditions, generalizing some recent results in the literature. Finally, numerical examples are given to illustrate our results.

Suggested Citation

  • Abdul Shakoor & Hu Yang & Ilyas Ali, 2013. "Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:804313
    DOI: 10.1155/2013/804313
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    1. Abdul Shakoor & Hu Yang & Ilyas Ali, 2013. "Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, December.
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